login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of (n+1) X (1+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
1

%I #7 Oct 19 2018 08:07:54

%S 21,51,129,339,921,2571,7329,21219,62121,183291,543729,1618899,

%T 4832121,14447211,43243329,129533379,388206921,1163834331,3489930129,

%U 10466644659,31393642521,94168344651,282479868129,847389272739,2542067154921

%N Number of (n+1) X (1+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.

%H R. H. Hardin, <a href="/A235877/b235877.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 6*a(n-2).

%F Conjectures from _Colin Barker_, Oct 19 2018: (Start)

%F G.f.: 3*x*(7 - 18*x) / ((1 - 2*x)*(1 - 3*x)).

%F a(n) = 3*(2^(1+n) + 3^n).

%F (End)

%e Some solutions for n=5:

%e ..0..1....2..2....0..1....1..1....0..0....2..2....1..1....2..2....2..2....1..1

%e ..0..1....2..2....1..0....2..2....1..1....0..0....0..0....1..1....2..2....2..2

%e ..0..1....1..1....1..0....0..0....1..1....2..2....2..2....0..0....0..0....2..2

%e ..1..0....0..0....1..0....0..0....1..1....1..1....0..0....1..1....1..1....0..0

%e ..0..1....2..2....1..0....2..2....2..2....2..2....1..1....0..0....1..1....2..2

%e ..0..1....0..0....0..1....0..0....1..1....1..1....2..2....0..0....1..1....2..2

%Y Column 1 of A235884.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2014